Abstract
We prove finite jet determination for (finitely) smooth CR diffeomorphisms of (finitely) smooth Levi degenerate hypersurfaces in mathbb {C}^{n+1} by constructing generalized stationary discs glued to such hypersurfaces.
Highlights
Let M, M ⊂ Cn+1 be C -smooth hypersurfaces
Our goal in this paper is to study such smooth CR automorphisms of smooth hypersurfaces in Cn+1
We show that for allowable hypersurfaces in Cn+1, one can invariantly attach a finite-dimensional family of generalized stationary discs
Summary
Let M, M ⊂ Cn+1 be C -smooth hypersurfaces. We recall that the complex tangent space. We show that for allowable hypersurfaces in Cn+1, one can invariantly attach a finite-dimensional family of generalized stationary discs. If the Levi form degenerates at some points, the conormal bundle admits complex tangencies, and the attachment of discs is more complicated We shall overcome this difficulty by constructing an associated circle bundle N k SP (a bundle over S1 × SP whose fiber at (ζ, p) is ζ k N p SP ) whose CR singularities allows for attaching discs which pass through the singularity with certain predescribed orders. Theorem 1.4 If M is an admissible hypersurface, there exists a k0 ∈ N and a finite dimensional manifold of (small) k0-stationary discs attached to M.
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